A skeptical look at the Special Relativity narrative | Sociology and Pure Physics | N J Wildberger
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- čas přidán 27. 07. 2024
- The usual story of Special Relativity (SR) is built from two Postulates introduced by A. Einstein in his famous 1905 paper "On the Electrodynamics of Moving Bodies" in which he subsequently derives the Lorentz transformations and introduces the mind-bending notions of length contraction, time dilation and mass expansion as (relative) speeds approach that of light. But does this story really ring true??
Here we look critically at this standard narrative, and show that there is in fact another hero to the story (!): Galileo Galilei who really had the critical understanding that underpins the subject. In fact we claim that SR is a relatively simple logical consequence of taking Galileo's Invariance Principle to heart and working out carefully and consistently the logical and necessary implications of it.
We consider also the important insights of W. Ignatowsky, along with P. Frank / H. Rothe, from around 1910 about Einstein's second Postulate. And clarify the very important distinction between the notions of "Hypotheses" and "Postulates" in pure physics. We see that there is a serious confusion currently about even the basic nature of the statements being proposed here.
And let's also boldly introduce a very uncomfortable truth: that "Einstein's Postulate" about the constancy and universality of the speed of light "c" in all inertial reference frames has serious logical issues.
There is a considerable amount of sociology surrounding this topic, and so lots to think about in this direction.
If you are interested to learn more, please have a look at my 2014 UNSW seminar entitled "Bats, echolocation and a Newtonian view of SR" along with my latest videos on Special Relativity in the "Classical to Quantum" series at the CZcams channel Wild Egg Maths. There I will be laying out in some detail an alternative, purely mathematical, approach to SR which circumvents the role of light, and clarifies that most of SR is actually an observational effect which necessarily follows from consistent application of Galileo's Principle.
A big thanks to my Patreon supporters, and to the Members of the Wild Egg Maths channel.
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Professor Wildberger I applaud you for yet another interesting video. I have watched your videos and lectures for a long time and always come away with some insight to think about. This video in particular begins to touch at the edges of a dirty secret in physics that also extends into how we daily engage the world.
First, though it seems implicitly obvious to me, it seems that in today’s informal discourses we have to explicitly state the implicitly obvious, so - the following is my opinion.
I am a retired physicist who had an experimental design career at a National Laboratory in the United States and have spent a long life in physics thinking about the philosophical implications of modern physics. I think that most modern physicists who think about the philosophical underpinnings of physics have to come to the conclusion that physics does not describe the world as it is but rather physics provides predictive models of the world.
As you are probably aware, physicists do not have the same degree of rigour in their thinking as do mathematicians. The caviler way we treat infinitesimals is proof enough of this point. Physicists, in my opinion, are driven by expediency rather than rigour. The ultimate success of a physics theory is whether or not it predicts how the world behaves under certain circumstances not how rigorously it was developed.
The question of whether or not a theory is a description of how the world is, is rarely discussed in physics circles, at least not in the ones I circulated in some 15 years ago. However, many modern physicists who do think about such things, have to conclude that physics is generating highly predictive models of the world that probably have no resemblance to how the world really operates. Ultimately, as Kant pointed out in Critique of Pure Reason, we can not know whether the interpretations, representations or models we derive from our experiences actual describe how the world really is.
All modern physicists know that their assumptions and theories are subject to the same shortsightedness that Euclid’s geometry postulates had. Newton’s theory of gravity was usurped by Einstein’s General Relativity which is but one of many examples in the history of physics that points out that the physics theories based on today’s narrow understanding of the world will probably be usurped by some broader understanding of the world in the future. So with the narrow scope of what we know at any given moment, intrepid physics theorists make pronouncements that they hope will not be proven wrong in some broader scope, at least during their lifetime.
It is far easier to explore all the possibilities of a mathematical theory than it is to explore all the possible circumstances involved in a physics theory. Your example of whether or not the physics of a Klingon ship is the same as our Earth physics is a perfect example of just how difficult it is to explore the full realm of physics theories. However. physics finds it expedient to act "as if" Earth physics is the same as Klingon physics, an assumption that has served the various space programs with vehicles traveling our local stellar universe well so far. Unlike mathematical theories, verification of physics theories have to be explored in the physical world requiring much larger amounts of resources than do math theories. I am thinking of how much was involved in building the Large Hadron Collider to test a few but fundamental physics theories. Though mathematics has a built in logical structure by which to verify a theory’s veracity in all cases, no such structure exists in physics because we can’t really know all the cases that might crop up in the world.
So expediency is at the heart of modern physics. More succinctly, we act “as if” our theories and concepts of the world actually describe the world, knowing there is no way to actually prove the world is as we interpret, represent or model it. We act “as if” the world is as we interpret, represent or model it because it is an expedient way of dealing with the world as we daily encounter it. In this last sentence I have expanded the scope of the “as if” philosophy from the domain of physics to the general way we operate in the world at large. In essence I would postulate that each of us have expedient ways of dealing with the world that are probably incompatible with how the world actually is. Most of the suffering we encounter in our lives can be traced to how the world actually is colliding with how we expediently are trying to deal with the world.
As an example of how we daily engage the world expediently, I offer up our judicial systems. Both our countries expediently accept that we each have free will in our actions. However, this is a hotly debated topic to this day with many illustrious modern thinkers tending to weigh in on the side of us not having free will. And yet for thousands of years we have built judicial systems and their attendant code of law, expediently acting “as if” we do have free will in our actions.
Mathematicians and scientists find it expedient to think there are real numbers and infinity. Physicists find it expedient to think there are atoms. I no more believe there are numbers and atoms than I do angels, but I find acting “as if” there are numbers and atoms to be an expedient way of viewing the world, one that with many associated assumptions, has lead to the massive expansion in math, science and technology we have at our disposal today.
To the degree that Special Relativity has made it possible to predict how the world behaves in a certain domain of physical phenomenon and has enabled a vast array of technological advancements, it is a physics success. But our world view, probably with Special Relativity’s help, will most likely expand to the point that a new theory will usurp it in the future.
This is all to say, don’t be too hard on us physicists and our lack of rigour. We are doing the best we can with the limited understanding of the world and the limited resources we have available to us to fully verify our theories.
As a final note, I will point out that I am not the first to describe the expediency of the “as if” philosophy. Though he would be the first to say he was not the first to describe this “as if” philosophy either, to my mind, Hans Vaihinger’s The Philosophy of “As If” (1911) is the first to succinctly and clearly describe this philosophy we all engage in on a daily basis.
I hope you will continue to skeptically poke at our mathematical and physics assumptions!
@dogtired1234 Thanks for a lovely comment. I think you are raising such interesting points that point to a need for a larger, almost philosophical framing of fundamental physics. Is it possible to know the way the world works? Or at least possible to describe some of its workings in a consistent way? How does logical clarity figure in judging whether some physical theory is valid , or useful? Thanks also for the reference to Vaihinger's work.
"You can't measure the velocity of anything!"
This is so refreshing!
I love you're making these videos!
What credo of conventional wisdom will this man challenge next?
Revolutionary of the mind!
I would like to better understand the significance of the units. The speed of light could be expressed as 1.8 megafurlongs per microfortnight - maybe even redefining the furlong to make it an exact value - or whatever units Klingons use, but I don't see how that changes anything fundamental. But maybe this will be addressed in the next instalment. Looking forward to it.
This is the first time I am exposed to Professor Wildberger's lecture! I can only say one thing : BRILLIANT! YES! This is a measurement problem! Congratulations Professor (or rather Bravo! in Galileo's language!)! Congratulations for a very refressing lecture!
Thank you Dimitri.
I only wanted to underscore an aspect I'm sure you are aware of:
when light travels through any medium other than a vacuum, its speed decreases based on the medium's optical density. Different materials have different refractive indices, causing light to slow down to varying degrees. For example, the refractive index of air is approximately 1.0003, meaning light travels slightly slower in air than in a vacuum. In water, the refractive index is about 1.33, so light travels significantly slower in water than in a vacuum.
The variation in the speed of light through different media is a fundamental concept in optics, influencing phenomena such as refraction, which is the bending of light as it passes from one medium to another.
So when do we get to use a metre stab for "water measurements"?
😉
Hi Prof! Loved it. Very remarkable find with that quote from Galileo -- I'd never heard it before, only the term 'Galilean relativity', which is hardly as evocative as the quote itself!
One thing I'd like to suggest for you to do, before you get too far into this series, would be to have a chat (maybe an interview!) with an actual Physicist who's knowledgeable in the mathematics, and perhaps also in the pedagogy of relativity (perhaps someone who's done some lecturing for undergrad physics courses), and thus someone who can see 'both sides' of this issue: 1) the hard math and the logical underpinning, and 2) the 'story' that we tell ourselves about relativity in the interests of teaching and popularization.
In particular, I think it would be useful to try to cultivate a more specific and/or precise vocabulary of some of the different terms that get thrown around, but which actually can have very specific (and often distinct!) conceptual meanings.
For example, in the initial stages of the video, you were pretty clear about not being able to measure the *_"absolute_* velocity" of any objects. But soon after, you started to lose that clarity when you were just using the more-generic word "velocity" -- to the point that, taken out of context, it would have sounded like you were saying something to the effect of "We're just totally helpless to measure the velocity of anything at all! ... " And a misguided viewer/listener might take that "..." to imply that "... And so those physicists don't know anything at all! They're all just puppets of NASA and their fake Moon landings! We can all see with our own eyes that the Earth is flat!"
Obviously (to you and me) I'm taking this to an absurd degree. And normally that would be unfair, of course. If not for the fact that there are -- LITERALLY -- people today who actually do believe that the Earth is flat. And they use arguments just about as silly as that one to bolster their beliefs to each other. And sometimes they take quotes from people, out of context, to try to show that "See? We're not the only ones, etc. etc."
I'm just saying that there's quite a bit of potential for being misunderstood when one takes an atypical position on a fundamental topic like this one, so having a good foundation of vocabulary for discussing it can cut through that confusion before it even starts. (As a mathematician, and having seen most of your videos, obviously you already are aware of that utility of good definitions! 😅)
And also, it might be a bit of a boost towards that purpose if you were to have a chat with someone in the field who's already got such a vocabulary handy.
Anyway, just my thoughts/impressions based on this particular video. Looking forward to the next ones!
Cheers!
Thanks Rob, that is a great idea!
Robert Edward Grant , - take a discussion about it with him
I should also remark that what is often termed "Galilean relativity" is associated with "Galilean transformations" which as far as I know were not enunciated by Galileo himself, but ought to be attributed more to either Newton or one of his contemporaries. This is an important point, as it turns out that the "Galilean transformations" are not really consistent with Galileo's principle.
@29:00 don't get too worked up. Both courses I took on SR and GR gave credit to Galileo. Most courses I have since audited do too.
Yep, Galileo's principle of Relativity was always mentioned in the courses I did and in all the text books. Actually it was Huygens who extended the principle of relativity for mechanics (crediting Galileo) in the form we would understand today. Galileo thought that natural motion was in circular around the Earth (and other planets).
There is a big difference between: 1. Here is Einstein’s Postulate (and Galileo had something in that direction earlier) and 2. Here is Galileo’s Principle. It’s called … proper attribution.
I thought for sure you were going to say Hilbert or Lorenz, but I suppose Galileo is also underappreciated in popsci discourse (and even undergraduate university coursework) of this subject
Fascinating. I actually agree with you about the observational effect. There is nothing magical there.
@22:10 I think you're twisting the story too much. The BIPM only define the [m] in terms of c after trusting c is a constant in vacuum. They're using the postulate to define the [m] measurement standard. Not the other way around. For most physicists c=1 in Natural units, and _that's_ the definition. The BIPM are only defining SI Units, nothing else. It makes sense since the SI "second" is the most accurate of all the SI units, since it employs nuclear clocks. So it makes sense to base the [kg] and the [m] on the SI [s] and some arbitrary number for c in [m/s] They could've said c=300000000 [m/s] to define the [m]. But that'd disrupt a few businesses and historical records too much, a bit of a headache.
I think we can agree that there's something questionable if "postulates" are involved in our definitions of units so fundamental to our scientific framework. And in this case, is it possible to actually use the "distance light travels in 1/299,792,458 second" definition of a metre in any kind of meaningful way? For example suppose someone proposes to make some super accurate linear accelerator which is 10 km long and it is crucial that the length is exact. Are they going to be employing one way light signals to calibrate this distance exactly? It feels to me like this definition is just window dressing.
Thank you for a very helpful lecture.
I think of programming in almost any setting, where even a "constant" might be returned by a function, and even a function with no parameters can refer to a potentially changing underlying context. And as much safety and sanity can be gained in programming by reducing the impact of invisible contexts, perhaps the universe doesn't work that way. Why exactly can't "c" be a function of velocity among other context? As you've argued here, I agree that it is a sociological artifact. We can easily imagine treating "c" as context dependent, while also from this observation being able to impute new, related measurements for other properties such as distance, time, etc. Great video!
You are misunderstanding what physicists are saying about special relativity.
Galilean invariance is fundamentally different from Einstein's. According to Galileo, space and time exist separately, and when you change reference frames velocities add up perfectly.
What Einstein proposed in 1905 was that velocities should not add up perfectly. He did so to explain the Michelson-Morley experiment, that failed to detect any change to the speed of light whenever Earth was moving with different speeds relative to the sun. Another motivation for this, which is in his paper, is Maxwell's equations. At the time people were proposing aether theories to obtain Galilean invariance from Maxwell's equation, and the entire point of Einstein's paper was to argue that there was no need for this, as Maxwell's equations did respect a different kind of invariance, if you accepted the speed of light as contant, and instead let space and time mix together.
I agree that his postulates are hypotheses that need to be tested, but this was already done. It was tested in the Michelson-Morley experiment, in 1905 he wrote another paper in mass-energy equivalence where the theory correctly predicted the loss of mass when radioactive atoms emitted radiation. More dramatically, it's regularly tested in today's particle accelerators, because when unstable particles go very fast, they go a much greater distance that you'd expect by their lifetime if time dilation did not occur.
When other physicists said the constancy of speed of light is not required in relativity, it's because shortly after Einstein published his theory, Minkowski figured out that the same could be derived if you considered time a dimension just like the spatial ones. This is completely uncontroversial. It's an equivalent, and often times easier way to derive relativity. Because space and time can be treated as fundamentally the same, you could use the same units. You could measure time in meters, for example. However, for practical reasons it's better to have two units. For this reason, the speed of light is defined as that, because the units are mere conventions in view of relativity.
I have given this answer to another comment, but it is important enough to repeat it: the so-called "Galilean transformations" that connect observations of time and space between two Newtonian frames of reference were in fact not introduced by Galileo, but later after Newton's laws of motion had been introduced. Newton's laws of motion and the attendant Laws of Conservation of Momentum and Energy are already at odds with Galileo's Principle. See my answer to erniefromsesamestreet1516
Thank you, professor, for the great ideas.
I read and re-read Mach's books and considering Einstein knew his works and was in connection with him, I've got the impression that the whole point of Einstein's effort was to extend the Galileo's principle to any kind of frames of reference. Not only there's no telling who is stationary and who is "really" moving when the motion is uniform, but the same stays for the non-uniform motion. Particularly, there's no telling if it is the Earth rotating and the universe standing still or is it the universe rotating and the Earth stands still. All the effects must be the same in both cases because only relative motion is physically measurable and therefore matters.
If we resort to the Galileo's picture of a ship, there would be obvious difference when you move in different directions if the ship was accelerating. But there would be no telling if it is a ship moving non-uniformly or there is a gravitational force acting on it.
Newton's bucket experiment is also worth mentioning, but maybe it's for another comment.
When one observes the velocity of a peak of a wave on the surface of a still lake, one sees that it is proportional to the square root of its wavelength, and affected by gravity, so depending on the altitude of the lake. When one observes from the bank of a flowing river, one sees the velocity of a peak of a defined-wavelength wave added to or subtracted from the river's flow velocity. Einstein didn't have clocks that allowed corresponding measurements for light, but we have such clocks today. How does a light particle have a wavelength?
Excellent work.
Thanks!
I find this very interesting, and I am looking forward to the next episode :) However, I am having trouble understanding "from where" a metric system originates if nothing is guaranteed to stay invariant. It can work in Cartesian dualism, where mind is passively observing and works fundamentally different than "empirical reality". But dualism is out of fashion for a reason, because it leads to solipsism which indeed is extremely problematic. So in an epistemic sense, because I am a monist (mind and external relity are of the same), I cannot make my world work without there actually being universal units. Keep up the good work, I love the channel
Absolutely fascinating stuff again on this topic, thank you, and please keep it coming - looking forward to the next instalment. I do have a couple of points I want to raise for discussion. The first is that I’m not sure I agree that light is behaving like sound or water waves rather than bullets fired from a moving train. Rather I think light is different to all of those. If you use sound in place of light, your measurements of time intervals will be affected by how fast you are moving through the medium that is transmitting the sound waves. There is a special distinguished frame in which the speed of sound is what we expect, and it is the frame in which there is no bulk motion of the medium in which the sound is propagating. Is this not strongly related to the historical discussions of the ether and the speed, of light? Light is distinguished because there appears to be no frame in which the transmitting ether is stationary (or equivalently in which the observer is stationary with respect to the ether) and so the conclusion is there is no ether and light has this special property that no matter which inertial frame you are in, it always has the same velocity. The second point is that let’s assume the paper you mention from 1910 is correct and the second postulate is not required to deduce the length contractions etc of special relativity. Then would that not then instead elevate the constancy of the speed of light back into a new and interesting fact that needs an explanation? (Now that we assume that it isn’t a postulate.)Or perhaps a better way of saying this is, as you rightly point out it never was a postulate it was a hypothesis, and if we now detach it entirely from special relativity, then it suddenly becomes a startling observation that we need to explain.
I am not saying that Einstein claimed that light is acting the same as water sound waves. It is just that the original form of his Second Postulate describes light measurements as behaving as water or sound measurements with respect to the distinction between a stationary and a moving source in a given fixed (stationary) frame.
I would even go further than say Galileo's physical equations predict Einstein's equations; I would argue Einstein's physical equations can be directly derived from them, because they are in fact the same:
Galileo's equations that define the physics of sound propagation and Einstein's equations which define the physics of light are similar. Add to this, the fact electromagnetic radiation which have shorter wavelengths is sensed as light and radiation with longer wavelengths is sensed as temperature...
I ask you: Is it maybe even possible that because there are certain wavelengths of radiation which effect living cells, which a living organism then attempts to repair as an adaptation -- perhaps there existed an era upon a relevant time scale, with an abundance of this short wavelength radiation which perpetuated the evolution of all organic cells, until the radiation somehow vanished or extended in wavelength to non-reactive energy bands ?
1. Physics similarities:
It is correct that there are similarities between the equations describing sound propagation and those describing light. Both are wave phenomena, and many wave equations share similar mathematical structures.
2. Electromagnetic spectrum:
The observation about different parts of the electromagnetic spectrum being sensed as light or heat is also correct. This is due to how our bodies have evolved to detect and interpret different wavelengths of electromagnetic radiation.
3. Cellular effects of radiation:
It's true that certain wavelengths of radiation can affect living cells. This ranges from beneficial effects (like vitamin D production from UV light) to harmful ones (like DNA damage from high-energy radiation).
4. Evolutionary hypothesis:
The suggestion about a potential era of abundant short-wavelength radiation influencing cellular evolution: While speculative, it's not entirely out of the realm of possibility. Here are four more points to consider:
a) Early Earth conditions: The early Earth had different atmospheric composition and potentially higher levels of certain types of radiation reaching the surface.
b) UV radiation and early life: Some theories suggest that UV radiation played a role in the formation of complex organic molecules that led to the origin of life.
c) Cellular repair mechanisms: Many organisms have developed DNA repair mechanisms, which could have evolved in response to radiation exposure!
d) Changing conditions: Over geological time, Earth's atmosphere and radiation environment have changed significantly.
However, here are the challenges to my hypothesis:
1. Timescales: The evolution of complex cellular repair mechanisms typically occurs over very long periods, while changes in radiation levels might happen more rapidly.
2. Persistence of repair mechanisms: If the radiation vanished or became non-reactive, we might expect these repair mechanisms to be lost over time if they were no longer beneficial.
3. Lack of evidence: Currently, we don't have direct evidence of such a specific radiation-rich era coinciding with critical stages of cellular evolution.
To further highlight the important interplay between environmental conditions and biological evolution, which proves my hypothesis, would require further research and evidence in the fields of astrobiology and evolutionary biology.
A Genius is deep with thought. Dr. Wildberger is a true
Professor Wildberger, I really enjoy your videos and I wanted to comment on what you've posted here.
Firstly, I agree completely with your statements on the first postulate, that it is essentially a restatement of Galilean relativity. As for the reason behind the (over-)acknowledgement of Einstein to Galileo, I can only suggest that it comes from Einstein taking Galileo's principle seriously (via Mach) and applying it to physics at a time when many others were busy suggesting absolute velocities and luminiferous ethers, such as Lorentz's own justification of the contraction that bears his name.
I think the reason that the "second postulate" is so often emphasised - and I have no evidence for this beyond my own experience studying physics - is that it is the biggest practical leap between Galilean and Einsteinean relativity, which is to say the Galilean and Lorentz transforms. It's a big change to calculation and isn't an immediately obvious consequence of the principle of relativity, even if it does follow from it.
While it is true that the second postulate follows from the first, my understanding is that it *only* follows from the first due to Maxwell's laws. (Presumably any laws of electromagnetism that describe the same waves as Maxwell's equations would work here too.) So in my view, SR really does have two fundamental statements:
(1) A law of physics is valid in any inertial reference frame, and
(2) Maxwell's laws of electromagnetism are valid laws of physics.
I said "statements" because, as you have said, they are better not called "postulates". I believe (1) is actually a *definition* of a law of physics. A law of physics describes the physical world in all inertial reference frames, putting aside any difficulties defining inertial frames for now. If your law of physics fails in an inertial frame, it is not a law of physics and is probably a special case of one: we can do no better than define how we would like to describe the world. (2) is then better called a clarification of (1) rather than a postulate. From a quick look at Ignatowski and Frank and Rothe it seems like their derivations are a lot more mathematical and rigorous than this physical justification. I'll have to check them out properly and see.
It's worth noting what you may already know, which is that without SR, (2) is actually false; Maxwell's equations do not work in Galilean relativity and this was the whole impetus to applying the Lorentz transforms in the first place.
Following from that, it's not hard to see that a constant c is a new prediction of electromagnetism combined with the principle of relativity. I really liked your explanation of the speed of light being independent of the speed of it's source like other waves and the question of exactly what is analogous for light to the medium of a water or sound wave leads me to another point, that I think "the speed of light" is a misnomer for c. I think it's much better named something like "the space-time constant". It has units of velocity, yes, but it really represents some fundamental relation between space and time.
That "the speed of light in a vacuum is constant" is equivalently stated as "the speed of waves in the EM field in space has a maximum value", which the actual result of the wave solution to the macroscopic Maxwell's equations. With no impedance to velocity - no mass and no dielectric field - c is the highest value it can reach, and because this follows straight from what we believe to be laws of physics (vacuum solutions to Maxwell's equations) we must apply the principle of relativity and find that it is true in all inertial frames. If my inertial frame and your inertial frame both agree that light is in a vacuum, we must also agree it is travelling at c, assuming we take electromagnetism to give valid laws of physics.
I had some questions about when you brought up units and measurement in the last part, but I assume you will answer those in your next video.
Thank you again! and apologies if I have just told you things you already know.
But wouldn’t a moving observer detect a different sound speed than a stationary one; this is not so for light.
That might be, but it is not really in the direction of Einstein's original Postulate 2. That just involved a single "inertial reference frame".
I'm not sure of the actual answer, but it might depend on how the observer detects the speed of sound. For instance, if -- like in Wildberger's 'Bats in a 1D Cave' example -- the observers can only use sound itself to measure speeds (in particular, not light or anything else) then perhaps a moving bat would *not* 'see'/hear a different speed of sound than a stationary bat.
But I agree that it's a good question, and I'd also like to definitively know the answer. Need to brush up quite a bit on my 'change of reference frames' math to work it out on my own.
@@robharwood3538 to my knowledge, based on courses in physics and specific courses in relativity, Galilean velocity transformation is an approximation. Special relativity introduces the Lorentz transformation. Hardly anything else has gone through more experimental verification than SR. But both classically and relativistically sound or other signals than light will not have the same speed on all inertial frames. Only the speed of light in vacuum is an invariant.
@@adurgh Have you seen Prof. Wildberger's videos on the 'Bats in a 1D Cave' scenario? In it he derives the same Lorentz-like transformation based solely on bats using echolocation rather than vision to establish their reference frames.
We're not talking about the actual speed of sound as we typically talk about it. We're talking about how such bats could *measure* the 'speed of sound' using only their sound-based measurement apparatus (a sound-based 'meter stick' and a sound-based 'clock'; see the bats video for details).
It is in analogy to Einstein's thought experiments with light-based clocks (light bouncing between mirrors, for example), to show that the same Lorentz-like transformations can be derived, with similar relativity-esque effects like length contraction and time dilation, but without basing the whole thing on light and the speed of light, but rather sound and the speed of sound (or any other signal-type, in the abstract).
If you haven't yet seen the 'Bats in a 1D Cave' video (there's actually at least two different videos deriving it; once as an informal video lecture, another as an actual recorded traditional lecture), then I'd recommend it. It's quite interesting, IMHO.
I'd like to get a take on the _principle of general covariance_ too, some say it has no physical content, but it is clear Einstein knew what he was after, he just did not quite get there since he lacked the tools. The problem is PGC is not a symmetry of any physical object, it just warps spacetime by re-labelling. I believe the *_physical_* content of GR occurs when there is matter-energy which curves otherwise flat spacetime, the symmetry is then the transformation which restores flat spacetime geometry. Orthodox GR does not bother doing that, it just computes things using the now curved spacetime.
Flat spacetime is then the physical invariant. Since matter warped the manifold there is now a symmetry with a physical meaning: geodesics on the flattened spacetime are no longer straight lines, or in modern gauge symmetry parlance, a gauge field had to be introduced to flatten the curved spacetime, and this gauge field adds the right terms to all the derivatives. Demanding covariance for these gauge fields is then physically meaningful. Lasenby, Hestenes, Doran, et al call this Gauge Theory Gravity (GTG). Demanding rotation gauge separate to position gauge invariance gives Einstein--Cartan gravity in the GTG formalism. It is a very nice formalism because since they recover a flat spacetime geometry they can avoid all the tensor index notation and work with frame-free intrinsic geometry (the spacetime multivectors and spinors).
i think general covariance itself has no physical meaning since it has heen shown that newtonian mechanics can be cast in such a form aswell (is it newton-cartan theory or something? I cant remember)
however the physical content of general relativy comes in the combination with the equivalence principle:
namely that it states that gravity itself is locally an artifact of using certain coordinates: we can always transform into a system in which gravity locally vanishes and normal special relativity is regained.
so GR is not just about general covariance: it makes a physical statement combined with covariance:
namely that gravitational effects can be transformed away locally - this is exclusove to gravity: electromagnetism doesnt admit that, although it also is formulated "generally covariant" in GR!
i hope this clears things up a bit
i recommend you read weinbergs book if you are interested - he had a very physical approach to GR that Inlearned tonappreciate alot after our prof basically forced us to read it for his GR lecture :D
Great video!
Thanks!
Newton's equations are Galileo invariant. Maxwell's equations are not. At the time everybody thought: there must be something wrong with Maxwell's equations. Actually it was the other way around. This is what Einstein recognised. I think this is missing in your discussion?
There is a very common misattribution involved here: the so-called "Galilean transformations" that connect observations of time and space between two Newtonian frames of reference were in fact not introduced by Galileo, but later after Newton's laws of motion had been introduced. (It might have been Newton himself, or perhaps Huygens that introduced these transformations, I am not sure). The reality is that Newton's laws of motion and the attendant Laws of Conservation of Momentum and Energy are already at odds with Galileo's Principle. People managed to conveniently ignore this rather obvious fact, on account of the obvious power of Newton's laws. However when Maxwell's equations were enunciated, the discrepancy became too obvious to ignore, and it was this that led Lorentz, and Poincare, to propose alternate laws (replacing the "Newtonian transformations") and which then motivated Einstein to formulate his version of SR. In hindsight, it was Galileo who was right all along.
Maxwells equations are Galilean Invariant if observed charge depends on relative velocity.
How would measure using yourself as the measurement?
The difference is that the water or air is stationary relative to the observer but Einstein says that c is the same even if the “medium” is in relative motion.
There is no "medium".
ItsBS channel covers how c measurement works and why that part of it is hollow, similar to what Norm explained about Usain Bolt, but with animations to show it more clearly.
@@user-gd9vc3wq2h Yes that's my point. If there were a "medium" Michelson-Morley would have found it as we'd be moving relative to it as the Earth changed its direction of travel round the Sun. The speed of sound or water waves does change when you are moving relative to the air or water, so the Galilean postulate only works if you are carrying the air/water with you in your inertial frame. Einstein is saying (and Michelson-Morley demonstrates) that the speed does not change even when you measure across empty space while moving uniformly across it at different speeds or directions.
The circular definition for speed of light in m/s seems irrelevant. Speed is "c". Units of measurement will depend on some reference frame. More curious is the whole discussion ignored time, which is integral to SR and certainly integral to measurements of velocity. Problems discussed about how its meaningless to measure "v" for ball bearings, electrons, or photons, seemed to disregard the need to establish the inertial RF for meaurement and that 2 different frames may have different results which is indeed the core idea of SR.
Galileo didn't know about the Coriolis force, but that's OK. He was doing his experiments on a moving ship bouncing in the waves.
If only he had had a record player. I think he actually did investigate this problem, but decided it was impossible to measure at the time. That had to wait for Foucault's pendulum
Well, Mach explained this effect as purely relative. One cannot tell if it is the Earth rotating and the universe standing still or is it the universe rotating around the Earth. All the effects would be the same in both settings. Can anyone think that if the whole universe rotated around the Earth it would not affect every pendulum on in the world?
Thanks!🎉
• Anecdotally, there is a remark about definitions in and that this author's default referent lexicon (Merriam-Webster's 11th Collegiate Edition, p. 613) gives that the adjective coined in AD-1912 "hypothetico-deductive" is specifically, "relating to, being, or making use of the method of proposing hypotheses and testing their acceptability or falsity by determining whether their logical consequences are consistent with observed data." and it is recalled the suffixes *nomy and *ology in that the etymon of the initial is "law", whereas that of the alternate/second/terminal is "discourse"/"discussion"/"dialogue"/"word- about" and that there is a dichotomy between techne- and episteme- in that one is deductive or scientific in the sense of certitude/confidence-of-veracity as, for instance the symbol of black or white box at the end of a proof or quad erad demonstrandum (QED) where there isn't possibility of doubt or second-guessing and "incremental refining" such as with the SI is preposterous and the other is inductive or probabilistic, and also noted is the prefix of eco (House), as in the etymon 'oikos' (Greek), with the working assumption that terms containing the suffix -ics are systematic, with, then (Given a hidden premise alluded to or implied) ecology and economy concerning the same subject.
• As an aside, from NIST Handbook 44, Appendix B is contained the statements, "Section 403 of Public Law 93-380, the Education Amendment of 1974, states that it is the policy of the United States to encourage educational agencies and institutions to prepare students to use the metric system of measurement as part of the regular education program." and that "The meter was originally intended to be one ten-millionth part of the meridional quadrant of earth." with this being at least 195.866728 μm greater according to Times[Times[Plus[Entity["Planet","Earth"][EntityProperty["Planet","EquatorialRadius"]],Entity["Planet","Earth"][EntityProperty["Planet","PolarRadius"]]],Power[2,-1]],(2 π)] (Given a multiplicand of (2 Pi 2^-9 5^-7) for the subtrahend, less unity) providing the quantity of Solar Planet Three/Earth's average great circle with radius 6367444.65 m giving a numerical value about 19 and one-half hundred-thousandths greater than SI unit 2.
• Also, according to the 3rd update from chapter two of the aforementioned work (Referenced within commentary to the Professor's 06 August 2023 video on Staff Notation, or musicological discussion (At about -10.006 Ms)), where it is claimed "They have also discovered that light travels differently along this axis than anywhere else. There are now two known different speeds of light." (p. 146) with the 21 April 1997 work from Physical Review Letters by a Ralston and the 12 May 1997 work alluded to in Time magazine referring to a physicist named William Purcell with respect to galactic astrophysical measurements or reports thereof, that the observed maximum or 'supremum'/upper-bound for the electro-magnetic force-carrier/photon is not absolute and later work or conferencing about this supposed 'esoteric researcher', whom I revere (Which is notable with respect to bias and incongruent conclusions according to erroneous arguments of authority), from AD-2015 relates to "Birkeland currents" and essentially concerns biology with respect to the galaxy as an entity that exhibits features of life (Of the nature of an organism, essentially).
• To paraphrase there is instantaneous or tachyon-type communication between galaxies and even across larger distances, with this usually chalked up as hubris or hootenanny with a correlation (Here merely mentioned as a speculation or potential hypotheses) between these stipulations and I have not reviewed these lectures as of yet.
Post-script: QuantityMagnitude[SetPrecision[Times[Times[Times[Table[Power[Times[UnitConvert[PlanetData[a,"Volume"],"SIBase"], Times[Power[\:03c0,-1],Divide[3,4]]],Power[3,1]],List[a,EntityList[EntityClass["Planet",All]]]],Times[\:03c0, 2]],Power[2,-9], Power[5,-7]]], 30]] shows the same technique applied to each of the major planets (Excluding the planetoids or minor planets, e.g. Pluto, here) with it merely being remarked that this of the manner of "adjust to fit" or ad hoc tweaking or gradually refining the system according to the results garnered from scientific instrumentation and that this does not accord, in my opinion, with anything such as the verbiage the A. Einstein purportedly utilized in and that it not being "logically sound" implies that there is a contradiction and this is, poetically speaking, a "fly in the ointment" in and that the initial analysis is not thorough-going and as such, beside other things, the entire model established according to these results or system of equations propounded on account of this apparent "deduction" is called into question and thus this seminal text is mooted.
1679th Tuesday
Decemis Kalendae
738857
Quod erat dū
Œcology. Œconomia
Thank you, prof. Wildberger, for an interesting video. I think that you ought not to be worried too much about credit due to Galilee. I have seen it acknowledged in different places in relevant literature that Einstein had merely generalized and modified his principle by extrapolating it from mechanics to electromagnetism. I also wish to recommend to you an excellent book by a relatively unknown, though very capable, Hungarian physicist, Lajos Janossy. The book's title is 'Theory of Relatively based on Physical Reality,' and it's from 1970. It is the most thorough and consistent neo-Lorentzain treatment of relativity that I know of. The main idea of the book is this: the Lorentz transformations come in two variants: change of coordinates and actual deformation following physical boosting of an object. What Janossy calls the Lorentz principle states that physical deformations due to motion with respect to the ether look the same as the change of coordinates derived from the relativity and isotropy principles. He compares it to a rigid rotation of points that can be canceled by suitability rotating one's coordinate frame of reference. I think that the main problem in contemporary understanding of relativistic physics is the reliance on 4D spacetime rather than on the concept of the light medium, which is three dimensional. People interpret the relativity phenomenon as a kinematic/geometrical feature of a spacetime container rather than as a specific and dynamical feature of the the propagation medium of light. It is, basically, the same kind of thinking that you oppose in maths: a satisfaction with floating and superficially elegant formalism replacing hierarchical understanding ultimately grounded in perception.
The "rigid" rods can be taken as finite crystals at definite absolute thermodynamic temperatures, relative to the triple point of water. The "calibrated" clocks can be taken as atomic clocks. Crystals and atomic clocks and the triple point of water are considered by quantum mechanics, which may be considered as universal. Einstein did not have access to atomic clocks. To measure the speed of light, one needs 'synchronized' clocks at source and destination of the light signal. The 'synchrony' should be set by 'symmetrical' mechanical motion from a common 'centre', not referring to light. The 'symmetry' of the mechanical motion should be checked for itself, before one sets out to measure the speed of light. Is the velocity of light with respect to the reference frame, or with respect to free space? It was a terrible mistake to move to defining things in terms of the speed of light.
Does this then apply to sound, Doppler effect? Heisenberg's uncertainty principle is another restatement of the obvious, lauded as a profound new discovery. Very similar reasoning to this.
Special Relativity is simply a theory of hyperbolic perspective which is also true according to the evidence. After you have “demolished” it, let’s see if we can do a similar demolition of elliptical perspective. Many geographers claim that the world is round. Time for a sociological analysis?
question: you mentioned one term I'm not familiar with: SECOND? What is a second? How is it measured?
Take your favourite Caesium-133 atom, rub, shake and squeeze it until it makes a specific hyperfine transition between certain states. Observe the electromagnetic field of the radiation emitted and count about 9.2 billion oscillations. The time needed for that is one second. See the details on Wikipedia; maybe you need some more devices, but you can buy them on the internet.
I think history also fails to credit Giordano Bruno since he came up with the first version of the boat experiment.
Also I want more physics videos!
There are lots of good points here but I think you confused yourself quite a bit (the material is, as you said, quite poor in terms of logic).
On postulate: I've no idea what it's official current definition is, you said it's identical to axiom, but it may not have been what Einstein had in mind in 1905.
"The constancy of the speed of light" is indeed not a conjecture (aka hypothesis, principle) it's a choice of unit (c=1), aka a definition, an axiom.
It is, in particular, logically equivalent to what you have on the board at 7:10.
It's more or less implicit in his 1905 paper, but he changed his mind soon after, insisting it's justified by an interferometric experiment.
Chances are, Klingons also use c=1, at least for some of their physics.
You said there is a big difference between c and s. Well, only in because in special relativity c=1.
You can also set s=1 and study say, the Earth atmosphere as a Lorentzian manifold. The speed of light, with this axiom, will depend on the air temperature of course.
This is like saying there is a big difference between the fifth Euclid postulate and the fourth. I guess there's a big sociological/historical difference but they are both axioms.
You said that "rods appear to contract", this is, at best, a poor description. They appear to rotate and deform because the speed of light is not infinity.
Coordinates are contracted by a Lorentz transformation, not rods, nor images of rods.
If I turn a map, I don't move objects represented on the map; I'm just turning a map. So it's the same thing when the rotation is hyperbolic.
"Does Wikipedia credit Galileo?": Well Wikipedia's page on Galileo's ship credits Jean Buridan, Nicolas Oresme, Nicolaus Cusanus, Clavius and Giordano Bruno.
If you're interested in relativity sociology then you may be interested to know that:
- Voight derived the Lorentz transformation to study sound (Doppler effect)
- Michelson didn't consider the Doppler effect
- Fresnel derived the ether drag coefficient by assuming the relativity principle
- Einstein's definition of special relativity as limited to inertial frame is now a "widespread misconception".
You state that ""The constancy of the speed of light" is indeed not a conjecture (aka hypothesis, principle) it's a choice of unit (c=1), aka a definition, an axiom." I doubt if you could get a lot of physicists to agree with this claim.
Thanks for the lecture. Let me ask you a couple of questions: Can we assume the following: is the ordered vibration of gravitational quanta the same as light? Is there a contradiction in direct experiments with this proposal? Thank you in advance.
You can assume that if you want to, but it's not reasonable. First, "gravitational quanta" supposedly are associated with gravitational waves, not with electromagnetic waves. So they are not part of SR, which this thread is about. Second, you should be a bit clearer as to what you mean by this "ordered vibration". Are the "gravitational quanta" thought of as a medium (some lattice? Ordered vibration presupposes ordered position) that allows the propagation of light? Then that would be the good old ether which has been abolished more than 100 years ago (in our frame of reference). Also, this would be hard to imagine because the "gravitational quanta", if they were gravitons, would travel at the speed of light, which would make it hard for them to constitute a medium for the propagation of light. Third, your idea would mean that if there are no "gravitational quanta" then light couldn't propagate. So, a region with low gravity, far away from all galaxies, say, would be dark - not primarily in the sense that it doesn't produce light, but mainly in the sense that it doesn't let light pass through it. Honestly speaking, all this doesn't make much sense.
You are so right about the "sociology" going on. It's reached a "fever pitch" in recent times. Very little of what is being taught can be trusted now in light of all of the social engineering happening.
Read a book
I thought the gist of SR was: Rocket 1 uses a flashlight to produce light, and then measures the speed of this light RELATIVE TO HIS REFERENCE FRAME. Rocket 2 looks at the same beam of light (from Rocket 1) and also measures its speed RELATIVE TO HIS OWN REFERENCE FRAME. According to Einstein, Rocket 1's measurement should always agree with Rocket 2's measurement of the speed of light. This can only mean that velocities do not add like we assumed growing up.
Thank You for exploring these questionable assumptions of SR. "How can I sell you this fine SR ?" is kind of like "How can I sell you this fine used automobile ?".
I have added a reference to Galilei in the Wikipedia article on special relativity.
Thanks Peter! That is great.
Strong stuff.
bravo Norman, looking forward to the next one in this series.
Have you seen the new paper that says the Hawkins-Penrose “Theorem” had a gap in its proof, so we don’t know if there’s a singularity in the centre of a black hole? I know it’s GR but fun to ask!
That article was from Kerr of Kerr Blackhole fame, so he is not against GR or blackholes lol
Singularities are actually dual!
The big bang is an infinite negative curvature singularity -- repulsive.
Dark energy is repulsive gravity or negative curvature -- hyperbolic, a pringle.
Gaussian negative curvature is defined with a minimum of two dual points -- non null homotopic.
en.wikipedia.org/wiki/Gaussian_curvature
So both positive and negative curvature singularities require two dual points.
Positive curvature is dual to negative curvature -- Gauss, Riemann geometry.
An infinite negative curvature singularity requires two dual points:- singularities are dual.
Spherical or elliptic geometry is dual to hyperbolic geometry.
You should read Julian Barbour's book about Janus points/holes.
Points are dual to lines -- the principle of duality in geometry.
"Always two there are" -- Yoda.
Energy is dual to mass -- Einstein.
Dark energy is dual to dark matter.
Space is dual to time -- Einstein.
Time dilation is dual to length contraction -- Einstein, special relativity.
Sounds interesting Fergal. Can you include a link to it so people can have a look? Thx.
@@hyperduality2838Did Einstein really call mass and energy - where is momentum here? - (resp. time and space) "dual" to each other? That doesn't make sense to me.
Black holes are a nonsense idea from the start. Relates to infinities, too. Schwarzschild's original paper was misinterpreted.
But what if Galieo dropped both a bullet and the moon from the Leaning Tower of Pisa? Would they fall at equal times, or...?
In college I asked, "How is light speed constant relative to the observer, and there is still a red-shift?" The professor wrote that basic transform on the board as if that was causal. That was ONLY a math expression, so it's only true on paper AFTER YOU CHANGE THE NUMBERS! So, Relativity CREATES ITSELF, and the non-transformed reality didn't disappear because you changed the numbers. All Gamma Ray Bursts arrive here in order of wavelength, and if that were known in the year 1900, there is no way Relativity would be here now.
bravo, you discovered the fraud that is SR
That transform ends up being a number between 0 and 1 that gets multiplied by length, mass, and time ADJUSTING THEM TO CREATE THE THEORY FOR YOU. It's like a ruse trick played on gullible humans who don't question math.
?? on the definition c= (wavelength)/period in System at rest= (wavelength)/period in S' "moving"! What is your problem?
@@krzysztofciuba271 My problem is √(1-v²/c²). As I said above. Do you understand what light speed constant relative to the observer means? Because, that should be an obviously crazy statement to make, but it is the only thing taught in schools, so if it's wrong, you will not see it. It takes effort on your part. After the transforms change everything (time included, yet there is no time), it says that if you move your head, then the entire Universe INSTANTLY changes length along that axis JUST FOR YOU. Don't even pretend like that makes sense. I want to see velocity addition experiments redone. In pion velocity addition experiments, I think they calibrated the experiment using assumptions of Relativity, then used the experiment to claim Relativity is correct. That's the same thing they did with muons. The CERN site used to say, "No matter how much energy we put into the fields to accelerate the particle, the particle never reaches the speed of light." How can you expect to push a car faster than you can run? If the limit is in the fields ability to push, then we have wasted 100 years on this GOOFY theory.
"@@jnhrtmn " ??? If you watch water-wave while at rest and the next while moving to the same water container the very water wave speed(group speed) is the same (as calculated by me) in both CS/coordinate systems! What don't you understand? ps. more nonsense you write though I agree the "particle" experiments are not properly explained in textbooks: one must use the wave model and point model to explain experiment data, otherwise, it mises ab.1/3 (1/"e"; e=2.7...) as the concept of "muon" refers to a statistical property that is normalized but that is not the case.
When the postulates were written down, they had _already_ been proven experimentally. Where did you get your physics training? How do you not know about the Michaelson Morely experiment? Interferometry is exquisitely precise.
The "one way" speed of light would break the first postulate. No direction is special. If it accelerated or decelerated over time, there would be a straightforward dependence on travel distance, and there is not.
Well there was the idea of aether drag so Dayton Miller did more precise measurements at higher elevations. He found some differences actually. Today the claim is that his results are still within experimental uncertainty in support of a lack of an aether.
@@SevenThunderful if there is an aether, then the rest of relativity doesn't make sense. It's the most thoroughly tested theory of all time. What is the problem that the aether is needed to explain? Why are we even talking about it? It's a goofy idea from a less mature era of science.
@@davidhand9721 And yet here we are with a defacto aether in the form of the space -time metric. There is no explanation for why c is a constant or why space and time warp in the presence of matter and energy etc.
Your comparison with Euclidean geometry is a bit strange to me. Euclidian geometry isn't self evident either. Or well, it's seemingly self evident but in the end it's also a hypothesis, right. You may go out into the world and ask could I find a triangle whose sum of angles is not pi. The point is that the notion of postulate is actually used in a similar way. Maybe Euclid didn't think of it like that. He might have thought that it was self evident. But serious modern physicists don't think the postulates of special relativity are self evident either. It's not even clear that they hold in that form on a deeper level. So these statements are mostly a set of rules that makes up a historical stepping stone for the development of physics. The ideas still play an important role of course. But special relativity is embedded in a much deeper way within quantum field theory and general relativity and ideas beyond those. There may of course be ideas at the speculative frontier where SR remains a central component and others where it does not.
Also, regardless of what mistakes of reasoning theoretical physicists who are expert on this topic may or may not make, the exact phrasing on wikipedia isn't really the most relevant data point for judging that.
The second Einstein postulate says that measuring the light speed you will obtain the same value, regardless of your speed. This is different for (much) slower objects (balls, electrons), when their speed can be defined only relative to your refference frame.
The speed of light also has to be defined with respect to a reference frame. Imagine a single photon travelling lonely through the universe and being oberved by several observers, each moving at constant speed wrt all others. All observers have their individual definition of the speed of this light particle, but the results of their measurements of this quantity will coincide.
It is worthwhile considering what direct evidence we have for the second postulate. Have we actually honestly measured the speed of light in even our reference frame? And what about the same question for some other frame?
@@user-gd9vc3wq2h In what way does our reading of 299,792,458 metres/sec coincide with the well known Klingon reading of 4155.37776 doodahs / quib ??
@@njwildberger The readings correspond because the conversion factors between the units are known. They have been found out as follows: One of our meter sticks and one of our clocks have been sent (carefully, without damaging them) to the Klingons' frame of reference. This meant an acceleration to the speed at which their space ship is traveling in our frame of reference (or, in their language, slowing down these objects until they are at rest). Then our clock has been compared to one of theirs with the result that the amount of time during which our clock advances by 1 second correspods to the amount of time during which their clock advances by some number N of quibs. Similarly, the meter stick has been aligned with the doodah sticks with the result that the length of 1 meter equals some number M of doodahs. So the conversion factor is 1m/s = M/N doodahs/quib. I trust you concerning the number you cited, so M and N must have been such that 415,537,776 N = 29,979,245,800,000 M.
After that, our clock and our meter stick have been brought back to us, set at rest in our frame of reference and compared with one of the other clocks and meter sticks, respectively. The result was that no difference could be observed, so both measurig devices have not been modified by this trip. In particular, these devices also were the same during the measurements performed while they were at rest in the Klingons' frame of reference.
(There may be other methods for getting an identical meter stick and clock in another frame of reference, e.g. sending precise instructions as to build them atom by atom, say, but I've been told they did it that way.)
@@njwildberger it's probably easier to measure differences in the speed of light, such as were sought after in looking for effects of the aether... There have been a lot of experiments looking for differences in the speed of light, as well as measuring the implications of an invariant light speed, eg time dilation. There have also been thoughts of a speed of light that changes over time, and how that would effect cosmological observation. The woman who could prove the speed of light to NOT be a constant would be a hero indeed! Of course one can say that nothing can be measured, and if it leads to something interesting, then by all means... The question of what can be measured may inevitably lead to quantum theory, which becomes very anti-intuitive, and perhaps does mark the end of the monkey brain's ability...
Einstein equivocates on his terms in the 1905 paper. Can you find the equivocation? A channel called "ItsBS" covers the issue pretty well.
The channel you cited seems highly dubious to me - at least what's asserted about Special Relativity. This should not be the level of discussion here.
You want to measure light speed? You got to use electronics. Now how does electronics act under relative motion?
@19:00 not sure what you are gonna say later, but at this point your take seems weird. There is obviously something very unique about light, which is that photons are massless spin=1. That's why their speed is universal. Same would be true for any classical massless field, it'd also propagate at c=1.
The presenter expresses the view that time dilation and length contraction are artefacts of observation. This is generally considered unsustainable on the basis of the muon synchrotron experiments, where the observed time dilation factor is given by the observed speed of the muons, which are moving at high speed on a circular path. This result is in accordance with the usual "clocks hypothesis".
Note that all inertial observers agree on the result, not just the observer comoving with the Earth, and they also all agree that the muons move faster and travel further (around a complete closed trajectory) than the Earth observer. Because all observers agree, it is an OBJECTIVE fact that fast moving clocks really do run slow.
We can also see this from the twins paradox, where all (inertial) observers agree on the objective fact that the twin who goes away and comes back ages less.
But why is it so? Why do moving clocks slow down? It is generally accepted that the energy from which massive particles are constructed, in the E=mc^2 sense, propagates at c. Every particle of matter is then a light clock, and we can analyse this by generalising the standard, 1D, light clock to 3 dimensions. See analysis in Section 7 here: www.academia.edu/30099390/Relativity_and_the_Luminal_Structure_of_Matter
Or we can easily understand time dilation, intuitively, without the math. To begin with, it is clear that no particle can exceed the speed of light: It cannot go faster than the energy it is made of. Next, as it approaches the speed of light, more of the movement of energy is required to transport the particle through space and less is available for internal evolution. So the internal evolution has to slow down.
While it is widely agreed that time dilation is a real physical phenomenon, the obvious question raised is just as widely dismissed: How to identify the condition of motion in which the clock runs fastest?
It's in the light. While light SPEED anisotropy for the moving observer is suppressed by the definition of simultaneity, there remains an observable DOPPLER SHIFT anisotropy, like this:
Consider two observers, Alice and Bob, located near to each other in a remote region of space. Assume that when she looks out of her spaceship’s windows, Alice sees an isotropically distributed universe: For her, the angular number density and brightness of astronomical objects is random, but independent of the direction in space. Let Bob’s velocity relative to Alice be 0.9 c. Although the available light sources are the same for both observers, the Doppler shift of light from any given source is clearly very different. Consequently, when Bob looks out of his spaceship’s window, the universe he sees is decidedly anisotropic: In the direction of his velocity relative to Alice, the stars appear far brighter and their number density is enhanced while, in the opposite direction, the stars appear dimmer and their number density is diminished.
This velocity dipole in the light reaching us from distant galaxies is an observed fact. See references here: www.academia.edu/38276250/A_Preferred_Frame_Thought_Experiment_Whos_Moving . It tells us how fast we are moving relative to the universe as a whole. Unless someone wants to argue that the universe as a whole is moving, it thus tells us how fast we are moving, period.
And there's another way. There is also a well known dipole anisotropy in the CMBR. This also tells us how fast we are moving (in this case relative to the centre of inertia of the local CMBR). Do these two dipoles agree? Yes, indeed, they do and it follows that both dipoles can only be induced by the motion of the detector as opposed to the various sources.
This well defined concept of our objective velocity through space also defines the "rest" condition, and we can now see that Einstein's undefined "Stationary system" is the unique inertial system that is in the condition of motion where the above velocity dipoles both vanish. Uniquely, for observers in this condition of motion, Einstein synchronisation really does synchronise clocks. For all other observers, it introduces synchronisation errors which combine beautifully with objective time dilation and length contraction to respect the relativity principle by inducing all the same well known, frame independent physical Laws.
The muon decay experiments are not inconsistent with an observational interpretation of SR. They are inconsistent with a classical Newtonian interpretation. They provide important confirmation of the likely validity of SR, and the essential correctness of Galileo's Principle. The Lorentz transformations are quite real and they can be observed, whether you have an observational interpretation of SR or a "lengths really are shrinking and clocks really are slowing" interpretation. (Sorry I don't know a better way to describe this position: is there a standard terminology?)
As for the twins paradox, that is not covered by Galileo's Principle, which only concerns itself with the relation between observations made by inertial observers moving uniformly with respect to each other. It is much better discussed in a GR course.
@@njwildberger No, GR isn't needed. You just need to analyse it the Special Relativity way: You must consider only from the point of view of (any) inertial observer. (The twin who goes away, turns around, changing to a different inertial frame, is clearly not one of those.) All inertial observers agree the one who went away ages less, so we have an objective fact that the time dilation is real, not just an artefact. One may consider for example a) the Earth observer, b) an observer who moves at the rocket speed away from Earth, and keeps moving in the same way throughout the whole experiment, c) an observer who moves at the rocket speed towards the Earth, and keeps moving in the same way throughout the whole experiment, d) any other inertial observer.
Of course the twin who goes away considers that his earthbound twin is aging slower on the outbound journey, and similarly for the inbound journey, but we don't care what he thinks: He is not a Lorentz observer in the Theory, so any calculations he may do regarding the trip as a whole are meaningless and inadmissible in Special Relativity.
@@njwildberger The system is putting these posts out of order. This one responds to your post three posts above.
Let's call it the "objective phenomena" point of view (i.e. clocks and rulers are velocity dependent instruments that undergo real physical changes upon a change in the condition of motion.). But I have no idea what you mean by "observational interpretation" of SR. Is there any other kind of interpretation, not just for SR, but Physical Theory in general? Perhaps you mean the point of view that there are no real physical changes in clocks and rulers involved, that they are not velocity dependent instruments, and time dilation and length contraction are artefacts of observation? Let's call this the "artefacts of observation" point of view.
The standard muon experiment - where we count them at the top and bottom of a mountain as they fly to earth - is compatible with an "artefacts of observation" point of view, but the SYNCHROTRON muon experiment is not. All inertial observers agree that they age less going around a loop than muons that are comoving with the Earth observer. There are three such objective (observer independent) facts: They age less, their average speed is greater than that of the Earth observer, and the distance they travel is greater than the Earth observer. All Lorentz observers agree. This is generally considered irreconcilable with the "artefacts of observation" point of view, but if you feel you can do that, please share your explanation how every Lorentz observer in the universe can agree they are aging less, but there is no real physical speed dependence of aging effect in play.
(The muons in the synchrotron and the twins are closely related. In both cases all inertial observers agree that they evolve slower when moving faster / travelling further. So these are objective (observer independent) facts. )
@@aa2ll260You claim that all inertial observers will conclude something or other about the twin who has accelerated. That however is not the case for an inertial observer who is only making conclusions based on Galileo’s Principle, as that principle simply does not apply to accelerated frames.
Einstein was trying to say that the speed of light being the same in all inertial frames falls out of the Lorentz equations (the inspiration behind special relativity), which, by constants, predict one and only one speed of light. If the Lorentz equations that describe electrodynamics are everywhere the same, then so, too, must be the speed of light*. That the laws of physics are the same in all inertial frames of reference is supported by Noether's theorem**, proven by Emmy Noether about seven years before that book came out.
*The speed of light in a medium appears to be an exception, but this is only because light does not directly propagate through media. Instead, intervening atoms absorb light and reemit it in all directions. But the speed of the photons scattering from atom to atom, like chips cascading down a plinko board, is still the speed of light predicted by the Lorentz equations.
**Noether made some assumptions about the uniformity of measurable quantities, but they are, prima facie, good, parsimonious assumptions. For example, all things being equal, Noether assumes that, regardless of how an object is rotated in space, its rotation-invariant measures, such as length and mass, will remain unchanged. ("Rotation-invariant" is a tautology here, but follows from parsimony and thousands of years of recorded human experience.)
"... whether these changes of state be referred to one or other of two systems of co-ordinates". But beware, a change of system of co-ordinates in the physicist's notebook is not a change of physical state of the system. As far as I can see, a change of state of the system requires some kind of acceleration. Also beware, Einstein supposes that the speed of light is isotropic in "empty space". He did not have available to him the GPS network of clocks and virtual observers. It seems from data from the GPS network that the speed of light is not isotropic, though we do not know convenient "empty spaces". Einstein used his idea of isotropy of the speed of light to base his definition of simultaneity on the speed of light. When it comes to testing his hypothesis of isotropy, he is left without resources. Another way of establishing isotropy would be to measure the one-way speed of light, using a principle of symmetry: identically constructed clocks, moved apart, along with separate observers, from a common starting point, by a symmetrical scheme of acceleration of clocks and observers, might be a way to establish simultaneity without depending on the speed of light. One might say that a symmetrical scheme of acceleration of clocks and virtual observers would be hard to achieve or trust. One would be right. But at least it can provide a testable and repeatable scheme, and will be able to show up its own defects of "symmetry", without assumptions on the speed of light. As I understand it, the GPS satisfies this requirement, at least to some degree. True, it uses light (radio waves), but it does a lot of cross-checking, that I think amounts to establishing symmetry, at least in some respects.
Using sound as a two-way time-space probe differs from Einstein in that sound has a definite medium of propagation which has a preferred co-ordinate system, in which the air is stationary.
re: czcams.com/video/ZCV73M3PcPQ/video.html , Einstein used the Lorentz transformations, but it was Lorentz who came up with the equation for x transforms. Poincare derived the equivalent for time and sent his work to Lorentz who published them.
Yes it’s important that Poincaré gets a prominent mention in this story too.
But changing units does nothing. The objective reality is the same wether klingons use meters or foots. In a very similar way I could use pooh igor and tiger faces instead of the 10 normal simbols for numbers and that would not change nothing but praxeological aspects. Its just a diferent way of summoning the same image on other peoples conceptual map. What im really keen on is whether objective reality changes for them due to speed difference, if i even have a well defined notion of "objective"
This presentation begins with two "quotes" from Einstein's 1905 paper. They are in English. The paper is written in German. Whatever translation he's using, it does not resemble the original. I know because I've checked the original German on precisely these two points. The English translation I have corresponds to the German as Einstein wrote it. Here is the passage which contains the postulates (in English):
"... the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. "
Unfortunately, the German pdf can't be copied and pasted here, but my bad German is good enough to see both texts are the same. You will not fail to note a vast difference between what Einstein wrote and what this presenter says he wrote. Key difference: There's no talk about any "stationary system" in Einstein's introduction. This is important not because the point he is making is wrong, it isn't, but because he has thereby butchered it completely.
You only have to look at the words on Einstein's page to go "OMG!!" He says "light is always propagated in empty space with a definite velocity c.....". Now once one misquotes this as "in the stationary system" there is by implication an observer. One is talking about a measured quantity for that observer. But there was no observer mentioned in Einstein's second postulate. Light moves through empty space at c, he wrote. What is this velocity, c, relative to? Empty space. It is exactly the same as saying a sound wave propagates through air at the speed of sound, or a water wave through water at the wave velocity. We then routinely find that the velocity of sound or a water wave relative to a moving observer is different for each observer, depending on his condition of motion.
What Einstein actually "postulated" was thus identical to the classical view of waves propagating in a medium: The wave velocity does not depend on the velocity of the source.
So, where does the modern "same for all observers" version of the second postulate come from? It comes from the definition of simultaneity. You can even see it in the video, where the light time from A to B is the same as from B to A. There is no good reason to expect that to be true INDEPENDENT of the condition of motion of the (comoving) points A and B. Classically, if A and B are moving at speed v relative to Einstein's "empty space", we'd have c+v in one direction and c-v in the other so T_AB = L/c+v ; T_BA = L/c-v. Not equal. From a classical point of view, the Einstein protocol does not synchronise clocks. But what do "synchronise" and "simultaneous" even mean?
Now Einstein, to his credit, states very clearly that (in order to define simultaneity) we must DEFINE that the light time from A to B is the same as from B to A. Since the distance is the same both ways, that DEFINES the light speed to be the same both ways, and more generally in any direction, for all observers. That's where it comes from.
So, not only did Einstein not say anything like the modern "same for all observers" version of the second postulate, but it was never ever a postulate (or hypothesis) only the consequence of a definition of simultaneity that would simply be wrong classically.
The obvious (but slightly dumb) question then arises whether there is any good reason to think it is valid relativistically: "Does Einstein synchronisation synchronise clocks?" While this question encapsulates the difference between relativity purists and sceptics, what informed people on both sides of the question agree is that the empirical validity and predictive power of the Theory does NOT depend on the answer (hence slightly dumb)......
Except for the quantum before-before paradoxes that is, including especially the forbidden causal temporal loops in the double Bell thought experiment. We thus now know that the Einstein protocol does not synchronise clocks. It just provides to observers an apparent simultaneity that is super powerful for making predictions simple.
None of the predictions changes, neither in Special Relativity nor in quantum mechanics, so this is "much ado about nothing" from a strictly Physics perspective. Nonetheless, we are free to restore some long dismissed intuitively appealing ideas: There is an objective fact of the matter about how fast a clock in a given condition of motion is ticking, about how long a ruler is, about the temporal order of spacelike separated events, and finally, we are once again entitled to talk about the state of the universe as it is "now".
www.academia.edu/39885176/After_PHYSICS
www.academia.edu/30099390/Relativity_and_the_Luminal_Structure_of_Matter
Please have a look at the English translation of Einstein's 1905 paper at www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf. At the bottom of page 3 he begins to introduce his two Postulates, and he does so on the next page, they are numbered 1 and 2 and I believe you will find them pretty much exactly as I quoted.
@@njwildberger I am pleased to find that the text you quote is from the paper. But you are in the wrong place..... after the sin has already been slipped in so to speak.
The link you give is the same translation I have. The postulates are introduced on page 1. Then we get the definition of simultaneity, and only then the text you are quoting, which began with:
"The following REFLEXIONS are based on the principle of relativity and on the principle of the constancy of the velocity of light. These two principles we define as follows".
The issue goes to the second one, right?
Note first that no "principle of the constancy of the velocity of light" was ever mentioned in the introduction.
Second, you will not fail to note that he now uses the definition of simultaneity from S1 above (which has ALREADY independently DEFINED the light speed to be constant for all observers) to define "time interval" in his velocity = distance / time formula for the "stationary" system, whatever that is.
Recall the definition: "We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A."
It is this definition of simultaneity that enforces the constant light speed for all observers, so there is no independent "principle" of the light speed constancy involved in this paper. The whole thing runs on the definition of simultaneity and the famous 2nd postulate is no more than a result of the definition.
That's why you should talk about the postulates that were actually introduced - in the introduction. By engaging with the circular definition (only available after slipping in the highly suspicious definition of simultaneity) all you do is muddy the water.
Now, the slippery definition turns out to work fine but it messes with peoples heads. It works fine in the Physics because it just so happens that the expression for the 2-way velocity of light at the end of S1 is an observed fact.
The messing with people's heads begins with observers in relative motion each thinking the other's clock is slow. One is entitled to ask how fast each clock is actually running, in an objective observer independent sense. What is the fact of the matter? When Physics insists that there is "no fact of the matter", that messes with peoples heads, as it should.
What I'd like to emphasise for you is that not only do we not need the 2nd postulate but also we do not need the definition of simultaneity. Nor do we need to mess with their heads. We only need the relativity principle.
Given the principle, all experiments work the same for all observers, but clearly, for that to hold all the various observers must perform their experiments in exactly the same way. In particular, they must all set up their clocks the same way. Einstein synch is one such protocol, where all observers follow exactly the same protocol. Slow transport is another. Subluminal projectiles is another. They all work the same. They all lead to Lorentz Transformations.
It is very simple. If you want frame independent laws out, you just need to put a frame independent clock setup protocol in. What you do not have to do is define simultaneity. It's redundant. Similarly, there is no need to claim that these protocols synchronise clocks. That's also redundant but it remains a core part of the doctrine. The part that causes all the confusion, dissent, paradoxes, and head messing. Take away the redundant claim that when observers in relative motion disagree there is "no fact of the matter" and the longstanding controversies over this Theory dissolve.
The German (onlinelibrary.wiley.com/doi/pdf/10.1002/andp.19053221004 p2) is:
Wir wollen diese Vermutung (deren Inhalt im folgenden “Prinzip der Relativität” genannt werden wird) zur Voraussetzung erheben und außerdem die mit ihm nur scheinbar unverträgliche Voraussetzung einführen, daß sich das Licht im leeren Raume stets mit einer bestimmten, vom Bewegungszustande des emittierenden Körpers unabhängigen Geschwindigkeit V fortpflanze.
This is exactly the same as the text you quote, up to the clausal ordering of the German, but is taken from the paper's Introduction. Norm is indeed quoting verbatim from the top of p4 (in www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf), which corresponds very well to the original German (p5):
1. Die Gesetze, nach denen sich die Zustände der physikalischen Systeme ändern, sind unabhängig davon, auf welches von zwei relativ zueinander in gleichförmiger Translationsbewegung befindlichen Koordinatensystemen diese Zustandsänderungen bezogen werden.
2. Jeder Lichtstrahl bewegt sich im “ruhenden" Koordinatensystem mit, der bestimmten Geschwindigkeit V, unabhängig davon, ob dieser Lichtstrahl von einem ruhenden oder bewegten Körper emittiert ist. Hierbei ist Geschwindigkeit = Lichtweg / Zeitdauer wobei “Zeitdauer” im Sinne der Definition des $1 aufzufassen ist.
I think everyone's confusion is actually about the word "moves" (bewegt sich) here, along with "in"! As you say, we can make copies of clocks and rulers, make our measurements, and check after our experiments that they still correspond, so there is never any issue about our units varying. On the other hand, as Einstein keeps saying, there is never anything meaningful, other than the collection of evidence recorded by a single observer, versus the collection of evidence recorded by another. The "stationary" frame Einstein refers to in 2. is just any arbitrary choice of observer, and the "stationary" or "moving" emitter is relative to that arbitrary choice of frame.
So Postulate 2 says for all observers O, when they measure the speed of light (using the method described), they always get the same number c, whether the light was emitted by a body stationary relative to O or moving relative to O. Also, the number is the same for any pair of observers O and O' in relative motion to one another, assuming they are measuring using identical clocks and rulers (checked before and after when O and O' are stationary relative to one another).
Thus there is an actual speed of light c, the number only depending trivially on the clocks and rulers used, any issue of "units" being settled when comparing clocks or rulers in the same (relatively stationary) frame.
Einstein postulates rigid rods. I suppose that they can suffer translative and rotatory motion. How do motion and rotation affect them?
How do we recognise an inertial frame? I incline to postulating that we have sensitive accelerometers constructed from strain gauges? I think this latter postulate needs to be stated explicitly and upfront.
I still want to use atomic clocks to define proper local time, though digital counts of the cycles of the light that they emit. They can also define proper local distance, if the local two-way speed of light is set as an arbitrary constant, perhaps for all inertial observers, and perhaps even for non-inertial observers. Physicists use the postulate of the constancy of the local speed of light, for all inertial observers, and even for all non-inertial observers; that's why they give it as an integral number of meters per second.
A light clock assumes that one has a standard mirror separation, and a knowledge of the speed of light.
I disagree that SR is difficult to understand. It really only has the one axiom. You apply the finite, constant speed of light, you get the right answer.
I don't get why an intertial frame of reference is one that's not accelerating (moving at constant speed). All motion is relative, there's no such thing as a non accelerating frame of reference because if for system A the system B is accelerating then A is accelerating from the virwpoint of B. An inertial frame of reference is one in which the laws of physics hold, then the general principle of relativity claims that all frames of reference moving at constant speed from an inertial frame are interial themselves too.
We know c is not a constant, it depends on the medium, not to mention the acceleration of the frame --- that's how gravitational lenses work
c is the speed of light ithe vacuum, and that it is a constant is an experimental fact.
As this thread is about Special Relativity, gravitational effects and accelerated reference frames are not to be considered.
btw, we don't know what mass actually is either :D
Yes, absolutely right. "Mass" is a hugely problematic concept which is swept under the carpet in so many even advanced physics discussions.
Same with force, point, length, distance, location, etc. There's not even one well-defined term in all of mathematical physics. I hope Norm covers more physics; stay-in-your-laneism is a desolate notion. Most of this is just basic reasoning anyway, but basic reasoning seems to confuse 99.9% of people.
@@ThePallidor I agree: each of those notions of force, point, length, distance, location and many others are far from being well-defined in physics. Sadly, discussions of SR and more advanced physics often completely finess the need for careful initial discussion to at least get these terms somewhat under control!
Your emphasis on Galilei's principle of relativity is certainly justified, but there is one point which in my opinion makes Galilei's principle of relativity weaker than Einstein's: all his examples are mechanical (jumping, throwing a ball); possibly he might even have thought of waves in his aquarium and maybe even of sound (as these are essentially mechanical phenomena). But I doubt he also would have applied this principle to light, since at that time the nature of light wasn't clear at all. Einstein's big merit here is to have driven Galilei's principle to its very end, with as a consequence that simultaneity is not an absolute notion any more, but dependent on the frame of reference. (As a benefit of this, as we know, comes that there is no need for some "ether" any more with all its unbelievable properties.)
If Galilei hat been told that his principle of relativity ultimately means that neither space nor time have an absolute meaning, he might have felt slightly over-interpreted.
I must interject in defense of Galileo and his clear right to priority when it comes to the basic Principle of Relativity, which belongs directly to him, and not to Poincare or Einstein. In defense of Einstein's claim, many will suggest, as you do, that Galileo's examples (from the quote I gave you) are mechanical, and hence do not cover more "modern physics" such as electromagnetism. But there are two problems with this. One is that of Galileo's examples, many, indeed most of them have a biological aspect as well as a mechanical one: the flying of birds, the swimming of fish, the throwing of a ball with a certain amount of effort, the jumping in different directions with again some given effort. Implicit in understanding these is the biological / neurological basis for how organisms generate motion, which we know these days has a strong electromagnetic aspect. Secondly, Galileo is referring also to the observation of these phenomena, so that the propagation of light signals in the ship's cabin is also part of the story here. Of course biology and electromagnetism had not been much developed in Galileo's day, but with his concluding statement "You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still" he is casting a very wide net. It is pointless to try to wriggle out of this by invoking the special nature of electromagnetism, just so that Einstein can keep the credit that has erroneously been given him for this most important of all physical understandings.
As I will show later in these lectures, or as you can see by watching my "Bats, Echolocation and a Newtonian view of Special Relativity" lecture (2014), the basic facts of SR are already quite apparent even in elementary mechanics once we adopt Galileo's position, and despite popular beliefs, the role of electromagnetism and light in establishing SR is a historical one, but not born of logical necessity.
But what is the speed of thought?
Generally …. slow.
It's real because when you travel to a place that appears from earth to be a light year away at a high speed almost c, the travel time on your watch can be made arbitrarily short as it's a function of the Lorenz factor.
So when was that done?
It's done in particle accelerators and by neutrinos every day.
@@deanrubine2955 And who accompanied the neutrinos while carrying my watch (or someone else's)? Where are the light years of distance in a particle accelerator?
Why does the notion of velocity with respect to a given inertial frame not make sense in your opinion? I suppose you know the usual story very well, since you sketched it at the beginning of the video. Space coordinates defined by identical rods, and time measurements performed by identical clocks, positioned at the points with integer coordinates and synchronized. Velocity with respect to this inertial system will be measured with these devices.
The "other" inertial system (i. e. the one in which the spaceship is at rest) will be equipped with exactly the same devices. If that's not the case from the outset, either they or we have to adopt the other's devices. In any case, this amounts to transferring at least one rod and one clock from one inertial system to the other. This will inevitably necessitate some acceleration, but after this transfer process, one still has the same rod and the same clock. (The behaviour of these devices is ruled by the laws of physics, which are the same in both inertial systems by hypothesis.) Of course, the spaceship will not travel at the speed of light or faster, but anything below warp 1 will be ok.
Where's the conceptual problem for you?
That's not really what I said: my main claim is that the notion of "velocity of an object" does not make proper sense. But to answer your question: the notion of "velocity with respect to a given inertial frame" perhaps makes sense as long as the units used on that inertial frame have been clarified. For example, it would not make much sense to me to ask: what is the velocity of a piece of space junk with respect to another piece of space junk? Unless that second space junk comes equipped with rods and clocks or something similar; and in that case the answer would be highly dependent on the nature of those rods and clocks, and we could not automatically assume that we know how to convert from those readings to ours.
@@njwildberger I think I see your objections, but I don't share them. Of course this "second piece of space junk" doesn't come equipped with rods and clocks, but it defines a frame of reference which could be equipped with these devices; even better: it could be equipped with devices identical to those we use in our frame of reference, which would avoid tedious conversions of units. With these devices, the velocity of the "first piece of space junk" could be measured, so this notion of velocity is well-defined. In my opinion, this velocity also is well-defined when the measuring devices are not actually there; in this case, it only would be difficult (or impossible to measure that velocity.
The speed of light *must* vary according to the local permeability and permittivity.
c = sqrt(mu * epsilon)
Moreover even if black holes existed, they would make the forward speed negative within the event horizon.
If black holes exist, the universe isn't a vector space and one can't do any meaningful physics with vectors and tensors …
@@peterjansen7929 I agree they don't exist.
@@whig01 They don't exist or vectors and tensors in physics don't exist. At least to me it seems overwhelmingly more likely that black holes don't exist (and certain, that there are no singularities), but the evidence false marginally short of absolute certainty. In any case, anyone wanting to point to even a slight hint at the existence of black holes would have to do so with a complete framework of mathematical physics that does not contain even a single vector!
And even then, one would have to distinguish between alleged black holes as a part of nature and merely nominal black holes as part of an extremely cumbersome formulation of laws of nature (rather like the Hollow World 'Theory', that is really merely a fanciful mathematically awkward description of observations, of no use to anyone who doesn't see complications as desirable in themselves).
@@peterjansen7929 Singularities are logically invalid.
@@whig01 Precisely! That's why it is ABSOLUTELY certain that there aren't any.
"You can't measure the velocity of anything". How did that work out for you whe you were stopped forcsoeeding, or in Australua, whem you got a ticket in the mail?
,, said a few minutes after paying homage to Galileo wbo wrote about velocity.
You are incorrect about the speed of light being constant due to a tautology. The constant nature of light speed was established by experiment, and this has been re-examined hundreds of times in ever-increasing precision over the years. It has never failed. Now that we know this for a fact, yes, we base the meter on c, but there is no sense in which the decision to do so is arbitrary.
Galilean relativity is _wrong_ regarding velocities. Velocities do not add. The precision with which this has been measured today is breathtaking. This was the point of special relativity.
I don't know where you got the impression that Galileo is not acknowledged, by Einstein or otherwise. In discussion of the first postulate, Galileo always comes up as the precursor among physicists.
Here is another scientist challenging the second ''postulate'': czcams.com/video/vp0rw9cxRbw/video.html
"The wheels on the bus go round and round." This song describes EVERYTHING you see a bus do EXACTLY like math does, but it is NOT an understanding of a bus. That would be causality, so this is the difference. I can show you causality in the gyroscopic effect. Angular momentum is like describing the bus: czcams.com/video/Sip_9ew2RjA/video.html Most cannot even see this, because CAUSALITY is foreign to their brain. This is basic mechanics wronged by math. The variables in gravity math are likely INCIDENTAL, NOT CAUSAL.
Relativity is not a social science: it is a description of the relationship between lines (world lines) drawn on a particular manifold (a spacetime manifold). Saying that we might write-down different numbers if we measure either with a meter stick or a ruler, is irrelevant. Measurements in one unit system can be transformed into measurements in any other system of units.
This is not a sociological question.
It is not really correct to think that measurements in one unit system can be transformed into measurements in any other unit system. This might be valid if both systems are with respect to the same observer: for example metres and feet for humans on earth. It is a much more problematic statement when applied to unit systems for different observers: for example metres for humans and doodahs for Klingons. This is analogous to the theoretical impossibility of comparing displacements in affine space if they are in different directions. To have a hope of doing that, we need a predetermined metric.
Ironically, when you describe velocities as "meaningless", I assume you mean _relative,_ you are stating Einstein's thoughts precisely. No frame of reference is special, but they can be measured relative to one another.
Place measurement devices in the object's path, making sure that they are at rest with respect to your chosen frame and that their clocks are synchronized. Connect the two with a rigid object of known length. When they detect the object passing through, they note the time. You can then collect the numbers, subtract, and then divide the distance by the difference. That is the relative speed.
The Lorentz transforms take in relative speeds as parameters and use them to convert events from one frame to another. This is exactly the same as Galileo's conception of velocity, but this time they give the correct answers.
Literally no one thinks aliens must be measuring in meters or seconds. You're really thinking about this all wrong. The speed c is a ratio between units; multiplying _any_ unit of time gives you the equivalent distance. This is why physicists often use "natural units" where c = 1. An alien can measure in any units it wants; we will always agree on velocities as fractions of c.
Here's how to avoid being deceived by a flawed view of reality, like Einstein was. You just consider it always to be your frame which is moving and the other frame to be stationary. Would a light clock tick at a different rate just because you flew past it? No, and neither would one in your own frame. If you fly past a light clock, keeping your eyes focused on it by turning your head as you pass by, why would it look any different? Einstein says you would see that other light clock ticking in slow motion, which would mean you see light moving in slow motion. Is that logical? You wouldn't see light taking a zig-zag path at all. It might look vaguely like that if you kept your eyes focused straight ahead, but why would you do that, and if you did you would simply be causing an illusion by doing it. That's obviously not what's really happening, the light clock isn't even moving, you are, so how could that affect anything about the light clock? Einstein simply couldn't comprehend the difference between an optical illusion and reality.
Do you mean to say that some people couldn't see that this is an observational effect 🤔 I got it straight away. 🌟✨️🎶💥
I would love to see a sociological survey of physicists on their view of whether say "length contraction" is a real effect or an observational effect, or perhaps something else. Any physics students/ professors care to wade in with their opinions on this crucial question?
? The" length contraction": in what CS/coordinate system? "At rest" or as you@textbooks imply in the "moving" CS but from the point of this CS "moving" the measurement devices(rods, clocks) are at rest!!!!@@njwildbergerThat is plain logic (Aristotle, esp. modified one by A.Tarski's scientific semantics, AD 1936 for formal-math systems but easily apply to natural science)
Thank you!
I don't see that the use of different units is quite as relevant as you make it appear. They can be compared and converted into each other. The numbers will be different but the quantities as such won't be. But the meaninglessness of "energy" as some absolute found in nature can't be emphasized enough!
"Energy can neither be created or destroyed." That's the kind of stuff that puts money in mystics' pockets. It gives credence to nonsense like "crystal energy". Energy is not a natural phenomenon, nor even a feature of natural phenomena. It is an invented accounting quantity that helps us perform calculations in physics. It wasn't found to be conserved but designed that way. The possibility of designing such a quantity at all is physically relevant, but that's a different matter altogether.
You have a gamma particle going by. So what's its kinetic energy? That's like being shown around an insurance office building and allowed to ask questions at the end, only to express disappointment that you weren't shown the free asset ratio.
We must be very careful about making statements about comparing unit systems for different observers. Yes, in a given inertial frame, we can quantify the relation between two units of the same quantity, say metres and feet for lengths. However for different unit systems in DIFFERENT reference frames the story is very different. It is not possible to consistently relate metres in say a human spaceship and “doodahs” in a Klingon spaceship moving with respect to us. This is a source of confusion in popular physics discussions, where often the incorrect assumption that all inertial frames are using metres and seconds goes unchallenged.
@@njwildberger True, but it had to be made clear that that was the intended meaning. Thank you for having done so now!
I've tried getting your attention before,,,I can prove math can be perfectly analogous and totally miss the cause. The variables in gravity math are likely incidental, NOT CAUSAL! Everyone thinks angular momentum causes the gyroscopic effect even AFTER knowing that it is a pretend vector representing a sum of smaller linear momentums. After the right-hand rule, YOU HAVE LEFT REALITY BEHIND. Look at my treatment with new math that describes the causal ACCELERATIONS. It is literally a force field of acceleration vectors with a center-mass that you can calculate. AND, understanding the cause led me to create a gyro using straight-lined motion. Angular momentum didn't do that for you, because your way is a math analogy.
Nathan is 4 CORNER simultaneous evil 4 TIME-Like CUBE funded by US TIME relativity!
The use Law and Principle interchangeably as well Sir!
But a Law is Universal while a Principle is specific!
And he never gave any proof for why volume goes to 0, mass to infinity and time to 0 as well... he just wrote down a faulty equation which makes no sense!
You almost ...got it at 18:25 but later you ..failed. Physically both systems: "at rest" and "moving" are the same,i.e., their measurement devices have the same unit, i.e.,"unit" = 1 meter or 1 second (the concept of 1 meter is useless in QM and astronomy; hence the MUST to quit Euclidean geometry and Galileo transformation as ... useless!)Yet, mathematically@geometrically (in textbooks) the symbols, x'(y',z') and t' of the moving coordinate systems S'(x',t') do not mean a measurement in S' but ONLY the value of them as seen from S(x,t) at rest! Hence, the Lorentz transformation is ONLY a mathematical fiction tool to calculate some parameters from the "moving system" or the parameters of "a closed physical system at rest" by a moving observer. It is a scandal that H.Minkowski, a mathematician, did not see it and claimed the space-time distance is path-dependent but it is contrary to the complex plane(x, it) main postulate (your other video on it confirmed visually to me that Minkowski's fault). Consequently, all the textbooks' explanations of Lorentz formulas are BS that fool only readers and students! You got it as the S' units are not "units" (of S) but the magnitude of the basis vectors that are not 1 but Lorentz constant "gamma"=1/((1-(v/c)^2))^(1/2).
Why are we allowed to assume that two inertial systems are the "same" in the sense of having measurement devices with the "same unit". And what would that mean anyway? One of the main points of SR is that we have to be very careful about comparing measurements in different inertial frames, even if they appear to be "the same". And that assumption is not necessary, as the Klingons for some reason refuse to use meters and seconds. In fact ... so do the Americans a lot of the time. :)
A. Einstein, Relativity,1916/1961:Appendix 1,p.116, more in M.Born.Einstein's Th.of Relativity,1965,p.252@other authors but...A.Einstein is not so clear on the unit of a clock; a very strange, hence is nonsense in 1905's article; a "peculiar consequence of a traveling clock" but this clock is at rest in his own reference system! Hence, Lorentz transformation is only a mathematical fiction of typical transformation between two reference systems (applied to Minkowski space) but..most physicists don't get it@@njwildberger. Sorry, "scientists" don't reason; they only...calculate!
Einstein in Harvey R.Brown, Physical Realtivity,2005,p.81:
In 1910, he was more explicit: ‘It should be noted that we will always implicitly assume that the fact of a measuring rod or clock being set in motion or brought back to rest does not change the length of the rod or the rate of the clock.’ 41
Again: it is proof of Einstein's right Theory assumption,i.e., the physical equivalence of both reference systems but the conclusion about a physical change in the "moving system" of time and distance is a conclusion contra his 1st Theory Principle: the physical law does not change in different ref. systems,i.e., there is no change in the dynamic nature of the system. The experiments with atomic clocks or radioactive decaying paritcles confirm the predictions of Theory only indirectly: the different gravitational potential (GPS, planes fly around Earth in gravitational potential), "muon"s experiment- at first seem to prove Lorentz formula for SR but I suggest it again proves GR: as Earth gravitation really has no influence (v.tiny- I calculated) but in a scintillator a traveling statistical "muon" experiences de-acceleration until it "stops" and mathematically both models of SR and GR give the same result (but in cyclotron they experience a radial acceleration to get higher speed as acceleration in itself has no influence on time in Lorentz formula)
To believe in Relativity, you have to believe that when you move your head, the ENTIRE Universe INSTANTLY changes shape along that axis JUST FOR YOU! That is too much for such little support. If muons entering the atmosphere are traveling faster than light, this support falls apart. There are other contradictions that are just NOT seen as contradictions. Time is only in your head (remember, anticipate), or it is a sequence counter in math. Send a pendulum into space and tell me about relative time. Dimensions 1 and 2 don't exist on their own, and the 4th is the same (sequence counter, a concept). Einstein made this 4th dimension adjustable, thereby caging humanity in this joke of a theory. Most people just follow and regurgitate. I watch your videos and I love them, so I hope I'm not offending you, but I am offended by this theory, not you.
Modern physics, modern math, modern art, and modern architecture are equally offensive and I don't think that's a coincidence.
LOL
Special relativity is just causality, can't go without it without rejecting causality
Galileo was a towering figure but you know, being excommunicated can hurt your rep, so blame the Pope, not Einstein
Two inertial frames can only be in constant relative velocity if they're both on the same path, meaning either on a collision course or the exact opposite, moving directly away from each other. If a frame is moving inertially along a straight path such that it will pass some distance in front of another frame, they're not in steady relative velocity.
The truth of this is easily shown by the doppler effect of a train whistle, it constantly varies as it passes in front of the observer who is at a station some distance from the track. If he was standing on the track, the sound would be a steady tone as it approached him and a different steady tone as it receded away from him, after he jumped off the track and back on to avoid being hit.
Point being, the Lorentz Transformation could not possibly work unless the observer is actually on the path of the other frame, because it's a single factor for a single velocity, not a constantly changing velocity. If the path was some distance in front of the observer then a clock in the other frame would have to be seen as running at almost the same rate as the observer's clock when far away, then gradually slowing down until it's directly in front of him and then gradually increasing again as it moved away, analogous to the gradually changing tone of the train whistle.
I am reading Galilée in Italiano. Everything you are saying is correct.
I have read Newton in Latin.
I read Einstein in Germany.
Of the 3 the Italiano is the finest mind and there is nothing the other two said that Galilée did not say first.
The only difference between the three is what Galilée said is the difference between he and those that came before him. Better instruments and more time.
18:24 You just don't understand the experiment. You cannot measure the speed of light without a detector which uses electricity which travels at the speed of light. If your tools work at all, then light is moving at c.
You don't need electricity to measure the speed of light. You only need two persons with synchronized clocks at two points A and B (not moving in your frame of reference). Take as long as you need to measure the distance d between A and B, to convince the person at A to emit a light signal (light a candle) at a specific time t_A and to convince the person at B to record the time t_B when he observes that signal. Now walk over to point B, get that information and perform the computation (t_B-t_A) /d. Voilà.
@@user-gd9vc3wq2h Clocks made of? Lol
@@ExistenceUniversityWhat clocks are made of doesn't matter at all. They only need to produce a signal periodically. A pendulum would do. The luxury versions have some kind of display that counts the number of signals.
@@user-gd9vc3wq2h I understand your hypothetical photon clock. You are saying what I am saying in smaller more laymen words. I am telling you that what that is at the higher level of investigation is that it is causality. In real life, your clock needs batteries. Your clock needs to interact with itself at the speed of virtual photon which is at c.
@@ExistenceUniversityI don't know whether my clock is a "photon clock" and whether it uses batteries or a mechanical spring. The only thing I know is that it produces a periodical signal. That such clocks exist and that they can be used to measure time in their inertial system is one of the basic hypotheses of mechanics, be it Galilean or relativistic (in the sense of Special Relativity). A second hypothesis on the same fundamental level is that there exist (rigid) rods that can be arranged in a spacially periodic manner in order to measure positions of points.
Thank you. I get tired of people saying that which Einstein did not say.
Some one here says Sir Stick to Maths.
I am not upset that such an impossible challenge was issued.
The person who issued that chalange is superstitious.
Why? The Pathagorians were a pagan religion that were really good a employing the first fields of the maths.
Astrology does a very good job based upon the monuments of the planets and stars that can be seen with the naked eye at predicting the future.
Numberoligy dose such a good job at predicting bad luck that few buildings have 13th floors.
The Modernist superstition says that to talk of anything but maths as they see them is wrong
What you are saying is that every cult uses the science of the day when the cult begins.
There are Modern Cults who claim their members are scientist who misappropriate maths to support their cult.
Postulates are not axioms, they are hypotheses, and they are tested, repeatedly.
@lordliege: you state that "Postulates are not axioms, they are hypotheses..." Can you explain then what the difference between the words "postulate" and "hypothesis" is according to your view?
@@njwildberger there is none, other than a degree of likelihood, they are suppositions, if then, axioms otoh are supposed to be intuitively obvious and need no proof, true in context, though different contexts may lead to different sets and conclusions
Einstein made such a mess.
Regarding moving source of light (or sound), SR claims that light is completely different than sound. With sound, if the source moves, it can catch up with the sound wave. The observer moving with the source observes c-v. With light, observer moving with the sources always observes c. The problem with SR is that it's not even wrong. It's a monumental mess.
And he was aware of it when he said,
"Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore."
Well nobody understands it, there's nothing to understand. Es ist nicht nur nicht richtig, es ist nicht einmal falsch Herr Einstein!
So did Heisenberg, Hilbert, and Bohr.
Sociology of physics 🤣🤣🤣🤣Sir please stick to mathematics. Many physics textbooks DO cover the fact that Galilei was aware of some aspects of special relativity. Textbooks like Shankar's (his videos are online on youtube on the yale physics channel) I suggest you read up on those undergraduate introductory physics courses before making claims that this is not known in the physics community...Because those claims are false.
I am not saying that it is not known in the physics community that the crucial insight of SR belongs to Galileo. I am saying that it is not universally acknowledged, and its fair to say that it is not even widely acknowledged. I find it interesting that you feel so strongly that just because I am a mathematician I should not be allowed to express an opinion on essentially logical and historical points of physics. Should physics be immune from any kind of Sociological scrutiny? That might be convenient to the gate-keepers, but we are living in open times when discourse on a wide variety of subjects is freely accepted.
@@njwildberger I kind of agree with both of you. I’ve seen Galileo mentioned/credited [“Galilean reference frame”] many times in the expositions of SR, but on the other hand not in the way you suggest or wish he rightly should be.
FWIW I find myself attracted to your stance on these things - there always seem to be points in any exposition of SR that beg for questions, yet the foundations are presented as solid. For example, the measuring rods are accelerated and decelerated as the frame is laid out. How do we know, for instance, that they’re not longer or shorter the further away they are because of that treatment [perhaps unsymmetrical, inelastic deformation from the forces exerted]? At such a point I accuse myself of unnecessary, petty nitpicking and tell myself to “get on with it!”. Still, the uneasiness of unanswered questions lingers, whether they’re meaningful and worthwhile or just dumb.
But then similar happens with Newton mechanics - for instance, a commenter here mentions the definition mass.
I remember at school early on in physics wondering if I were alone in a vast empty universe how I would know whether I were rotating or not. With outstretched arms, a rocket in each hand firing in opposite directions and the end of a weighted spring balance between my teeth maybe that would tell me. But then what would it *mean* to be rotating? Rotating with respect to absolutely nothing! “Enough - you’re wasting time. Move on!” 😁
I’m looking forward these explorations of yours. Thank you. As for free and open discourse, YES! I’m with you there. 👍 I’m an absolutist on that one.
I know David N Mermin has a piece entitled “Relativity Without Light” but it’s behind a paywall. And he’s not the only one IIRC. A ‘popular’ version of it might be in his book “Boojums All The Way Through” but I can’t get to that right now. I must check. That was years ago though and my memory is not exactly reliable.
@@orsoncart802 Your point about the measuring rods of inertial frames being accelerated and decelerated as the frames are supposedly laid out is an excellent one. In my opinion, the resulting notion of an inertial reference frame is highly questionable, and seems but a remnant of Newtonian thinking, hanging on despite all the evidence that this framework has very little to do with the way we actually go about measuring in our local corner of the universe. It is much preferable to admit to the obvious: that we are essentially point observers and all measurements are coming to us from some kind of radiation or streams of particles. Vast networks of rigid rods, and observers with clocks equally spaced around the solar system / galaxy ?? I don't think so.
Shankar and I were classmates